Article Digest:
The slang term "flicks" for motion pictures originates back in the early days of movie making and projecting. Before the late 1920's, movies were made by exposing photographic film at a rate of about 16 frames per second. "About" is a very important word here, since movie cameras were operated by turning a hand crank, so the actual speed at which the film moved was anywhere between 8 and 22 frames per second (sometimes for stylistic reasons, sometimes because the camera operator got tired or too excited). Eventually, the playback of the film was standardized so that projectors ran the film at 16 frames per second.

To make the image look like it was a bunch of continuous pictures instead of a roll of pictures scrolling across the screen, a shutter was employed to blank the screen while the film was ratcheted so that the next frame would be displayed. Naturally, since the film was running at 16 frames per second, the shutter opened and closed at a rate of 16 cycles per second. The result was a constant flickering that was no doubt annoying. This led to the motion pictures being referred to as flicks.

It is commonly believed that the human eye cannot detect flicker at frequencies greater than 17 Hz, but this is not true. Flicker continued to plague the movies even after frame rates were increased to 24 frames per second (to accomodate the audio sound track). Even at 24 frames per second, flicker is apparent. The solution? Modern movie projectors close and open the shutter an extra time while projecting a single frame. The result is that each frame is actually displayed twice at the rate of 48 frames per second. At these frequencies, most people cannot discern the flicker caused by the cycling shutter.

I have no idea but my WAG is that it's a reference to early film and animation, using flickbook-type technology. It could also be a reference to the flickering of early film images. Or maybe it's because flicks rhymes with pics. Given the lameness of these suggestions, it doesn't take a genius to work out that I can be arsed to google.

flick
mid-15c., probably imitative of a light blow with a whip. Earliest recorded use is in phrase not worth a flykke "useless." As slang for "film," it is first attested 1926, a back formation from flicker, from their flickering appearance. The verb is first recorded 1838; meaning "quick turn of the wrist" is from 1897, originally in cricket. Related: Flicked; flicking.